Steady-state transverse response of an axially moving beam with time-dependent axial speed

Abstract

This paper investigates the non-linear dynamics of an axially moving beam with time-dependent axial speed, including numerical results for the non-linear resonant response of the system in the sub-critical speed regime and global dynamical behavior. Using Galerkin's technique, the non-linear partial differential equation of motion is discretized and reduced to a set of ordinary differential equations (ODEs) by choosing the basis functions to be eigenfunctions of a stationary beam. The set of ODEs is solved by the pseudo-arclength continuation technique, for the system in the sub-critical axial speed regime, and by direct time integration to investigate the global dynamics. Results are shown through frequency–response curves as well as bifurcation diagrams of the Poincaré maps. Points of interest in the parameter space in the form of time traces, phase-plane portraits, Poincaré maps, and fast Fourier transforms (FFTs) are also highlighted. Numerical results indicate that the system displays a wide variety of rich and interesting dynamical behavior.